SLICE pumpkin in half AND CLEAN it, removing all the seeds and fibrous strings using a large metal spoon or ice cream scoop.
COOK it! This is the best way to make all the peeling go much easier and quicker. If cooking in a MICROWAVE, place pumpkin half cut-side-down on a microwave-safe dish with a bit of water in it. Microwave one of the halves until the skin can be sliced away easily. Time varies depending on the size of the pumpkin as well as microwave wattage. My medium-size pumpkin took 18 minutes (100 % cooking power) in a 1100 watts microwave. It is fully cooked when fork tender (or it can be easily pricked with a toothpick).
If cooking in the OVEN, place clean pumpkin half or halves cut side up on a baking sheet (if pumpkin is large, you will have to bake halves separately) and bake in a preheated oven at 375º F for about 15 minutes (small), 30 minutes (medium), 45 minutes (large), or until fork tender.
LET COOL just enough to handle without burning your fingers.
PEEL it using a knife or your fingers. Either chop or purée the pumpkin flesh, depending what you are using it for. If you intend to purée, pumpkin can be cooked longer, making it much, much easier to peel the skin.